1. Field of the Invention
The present invention relates to a technique for analyzing light intensity distribution on an light exposure area where a mask pattern will be projected.
2. Description of the Related Art
A semiconductor device manufacturing process includes the photolithography step of shaping a photoresist film formed on a wafer into the desired form by a patterning technique. In this photolithography step, as illustrated in FIG. 4, light coming from a light source 11 passes through a mask 12 and is thereafter condensed by a lens 13 so as to be projected onto the photoresist film 14 formed on the wafer 15. However, the resultant resist pattern on the wafer 15 does not always have the same shape as a pattern printed on the mask 12. In consideration of this, the pattern needs to be printed on the mask 12 so that the resist pattern projected on the wafer 15 will be within an allowable design range.
To this end, the correspondence between the pattern printed on the mask and the resist pattern needs to be grasped. According to a conventionally known method, the intensity of light which will be projected on a light exposure area of a wafer to be exposed to light is analyzed through simulation, without the photoresist film being actually subjected to light.
The document xe2x80x9cY. C. Pati. et al. J. Opt. Soc. Am. A/Vol. 11, No. 9, 1994 xe2x80x9d discloses a light intensity calculating method for use in the case where the optical simulation of a stepper optical system, which is a kind of light exposure apparatus, is executed as such photolithographic simulation. According to the OCA (Optimal Coherent Approximation) method disclosed thereby, the light intensity (x, y) at the position specified by coordinates (x, y) on the light exposure area of the wafer is expressed by Equation (1) shown below:
I(x, y)=xcexa3xcex1|(Fxc3x97xcfx86)(x, y)|2xe2x80x83xe2x80x83(1)
where xcex1 and xcfx86 represent optical kernels determined by the stepper optical system (light exposure apparatus), F represents the transmission factor of the mask, and (Fxc3x97xcfx86(x, y) is the convolution integral of F and xcfx86.
A conventional light intensity analyzing method which adopts Equation (1) shown above will now be described with reference to the flowchart of FIG. 5. The process shown in this flowchart is executed by an information processing apparatus such as an engineering workstation.
Firstly, the kernel xcfx86 corresponding to each set of coordinates (x, y) on a wafer surface area when divided into a grid of areas at predetermined grid intervals dxf, are calculated and stored in a table (a step S201). The kernel xcfx86 is a value representing the extent of the mask which optically influences the coordinates (x, y) on the wafer. A rectangular area (Skxc3x97Sk), which has the size (Sk) equal to the kernel xcfx86 associated with a given set of coordinates (x, y), and which is located at a position corresponding to that specified by the given set of coordinates (x, y), is cut out from the mask pattern (a step S202).
Next, data representing the shape of the mask is developed into a bit map at grid intervals dxf, and the transmission factor F of the mask at the rectangular area is obtained (a step S203). The convolution integral (Fxc3x97xcfx86) (x, y) of the transmission factor F and the kernel xcfx86 is calculated and the calculated integral is adopted in Equation (1), thus obtaining the light intensity I (x, y) at the position specified by the given set of coordinates (x, y) on the wafer (a step S204).
Thereafter, it is determined whether the light intensities I (x, y) at the positions on the wafer, which positions are specified by all sets of target coordinates (x, y), have been calculated or not (a step S205). If it is determined that the light intensities I (x, y) at the positions specified by all sets of target coordinates (x, y) have not yet been calculated, then the same calculation as that described above is performed in connection with the position specified by the next set of coordinates. On the other hand, if it is determined that the light intensities I (x, y) at the positions specified by all sets of target coordinates (x, y) have been calculated, the entire light intensity distribution is output as the result of the analysis (a step S206). Then, the process shown in the flowchart is terminated.
However, in the case of analyzing the light intensity distribution with the conventional method described above, the grid intervals dxf at which the shape of the mask is developed into the bit map needs to be set at a satisfactorily small value in order to correctly evaluate the shape of the resist pattern which will be formed on the wafer. When calculating the convolution integral of the transmission factor F in connection with each of the rectangular areas divided at fine grid intervals set at such a small value, the calculation time is considerably long and the time required for the analysis is accordingly long.
Japanese Patent No. 2531114 and Unexamined Japanese Patent Application KOKAI Publication No. H9-237750 disclose light intensity distribution analyzing methods intended to reduce the time required for the analysis of the light intensity distribution. However, according to the methods disclosed thereby, the light intensity distribution is analyzed using Fourier transform. The techniques disclosed by the above patent and publication cannot be adopted as they are in a method for calculating the light intensity through utilization of the convolution integral.
It is accordingly an object of the present invention to provide a method and an apparatus which are capable of analyzing the light intensity distribution on a light exposure area within a short period of time, and a computer program product including a computer usable medium which contains a computer readable program embodied therein for the analysis of the light intensity distribution.
According to the first aspect of the present invention which aims to achieve the above object, there is provided a method for analyzing light intensity distribution on a light exposure area where a shape of a mask pattern will be projected through an optical system by exposure light coming from a light source, the analyzing method comprising:
dividing the light exposure area into first areas at predetermined first intervals;
cutting out first portions of the mask pattern which correspond to the first areas;
sequentially determining whether transmission areas which transmit the exposure light and non-transmission areas which do not transmit the exposure light are mingled at the cut-out first portions of the mask pattern;
calculating intensities of light which will be projected on the light exposure area, through use of the first portion of the mask pattern, when it is determined that the transmission areas and the non-transmission areas are not mingled; and
dividing each of the first areas into second areas at second intervals smaller than the first intervals and calculating intensities of light which will be projected on the light exposure area, through use of second portions of the mask pattern which correspond to the second areas, when it is determined that the transmission areas and the non-transmission areas are mingled.
According to the above method, only in the case where the transmission areas and the non transmission areas are mingled at the first portions of the mask pattern, the light intensity is calculated through use of the second portions of the mask pattern which correspond to the second areas into which each of the first areas have been divided. In the case where the transmission areas and the non transmission areas are not mingled, the light intensity is calculated through use of the first portions of the mask pattern which correspond to the first areas. Because of this, the number of times the light intensity calculation is performed to analyze the light intensity distribution over the entirety of the light exposure area is reduced. Accordingly, the time required for the analysis of the light intensity calculation is reduced.
In the above-described method, each of the first areas has a shape of a rectangle with four sides each being 100 xcex/NA to 200 xcex/NA (nm) in length, while each of the second areas has a shape of a rectangle with four sides each being 10 xcex/NA to 20 xcex/NA (nm) in length, where xcex presents a wavelength (nm) of the exposure light, while NA represents an numerical aperture of the optical system.
The above method may further comprise cutting out the second portions of the mask pattern which correspond to the second areas from each of the first portions of the mask pattern, after cutting out the first portions of the mask pattern. Determining whether the transmission areas and the non-transmission areas are mingled at the first portions of the mask pattern may be performed by determining whether areas having a transmission factor of 0 and areas having a transmission factor of 1 are mingled at the second portions of the mask pattern.
The above-described method may further comprise calculating all optical kernels xcfx861 corresponding to the first areas; and calculating all optical kernels xcfx862 corresponding to the second areas.
The optical kernels xcfx862 may be calculated by performing primary interpolation based on the optical kernels xcfx861.
The light intensities I (X, Y) at the positions specified by coordinates (X, Y) on the first areas and the light intensities I (x, y) at the positions specified by coordinates (x, y) on the second areas may be calculated respectively by:
xe2x80x83I(X, Y)=xcexa3xcex1|(Fxc3x97xcfx861)(X, Y)|2xe2x80x83xe2x80x83(1)
I(x, y)=xcexa3xcex1|(Fxc3x97xcfx862)(x, y)|2xe2x80x83xe2x80x83(2)
where xcex1 represents optical kernels, and F represents transmission factors of the first and second portions of the mask pattern which correspond to the first and second areas.
When the light intensities I (X, Y) at the positions specified by the coordinates (X, Y) on the first areas are calculated, the light intensities I (x, y) at the positions specified by the coordinates (x, y) on the second areas corresponding to the first areas can be given as I (X, Y).
The above-described method may further comprise: storing, in a predetermined table, the calculated intensities of light which will be projected on the first areas; storing, in the predetermined table, the calculated intensities of light which will be projected on the second areas; and outputting contents of the predetermined table as light intensity distribution analyzing results when light intensities over an entirety of the light exposure area have been stored in the predetermined table.
According to the second aspect of the present invention which aims to attain the aforementioned object, there is provided an analyzing apparatus for analyzing light intensity distribution on a light exposure area where a shape of a mask pattern will be projected through an optical system by exposure light coming from a light source, the analyzing apparatus comprising:
a storage unit which stores a program for dividing the light exposure area into first areas at predetermined first intervals, cutting out first portions of the mask pattern which correspond to the first areas, sequentially determining whether transmission areas which transmit the exposure light and non-transmission areas which do not transmit the exposure light are mingled at the cut-out first portions of the mask pattern, calculating intensities of light which will be projected on the light exposure area, through use of the first portions of the mask pattern, when it is determined that the transmission areas and the non-transmission areas are not mingled, and dividing each of the first areas into second areas at second intervals smaller than the first intervals and calculating intensities of light which will be projected on the light exposure area, through use of second portions of the mask pattern which correspond to the second areas, when it is determined that the transmission areas and the non-transmission areas are mingled;
a processing unit which sequentially executes the program stored in the storage unit and analyzes the light intensity distribution on the light exposure area; and
an output device which outputs a result of analysis of the light intensity distribution analyzed by the processing unit.
In the above-described apparatus, the storage unit may store mask patterns. In this case, the apparatus may further comprise an input device which selects a desired pattern from among the mask patterns stored in the storage unit, and the processing unit may perform processing in accordance with the mask pattern selected by the input device.
According to the third aspect of the present invention which aims to attain the aforementioned object, there is provided an analyzing apparatus for analyzing light intensity distribution on a light exposure area where a shape of a mask pattern will be projected through an optical system by exposure light coming from a light source, the analyzing apparatus comprising:
means for dividing the light exposure area into first areas at predetermined first intervals;
means for sequentially determining whether transmission areas which transmit the exposure light and non-transmission areas which do not transmit the exposure light are mingled at first portions of the mask pattern which correspond to the first areas;
means for calculating intensities of light which will be projected on the light exposure area, through use of first portions of the mask pattern, when it is determined that the transmission areas and the non-transmission areas are not mingled; and
means for dividing each of the first areas into second areas at second intervals smaller than the first intervals and calculating intensities of light which will be projected on the light exposure area, through use of second portions of the mask pattern which correspond to the second areas, when it is determined that the transmission areas and the non-transmission areas are mingled.
According to the fourth aspect of the present invention which aims to attain the aforementioned object, there is provided a computer program product including a computer usable medium which contains a computer readable program embodied therein for analyzing light intensity distribution on a light exposure area where a shape of a mask pattern will be projected through an optical system by exposure light coming from a light source, the program executing:
dividing the light exposure area into first areas at predetermined first intervals;
sequentially determining whether transmission areas which transmit the exposure light and non-transmission areas which do not transmit the exposure light are mingled at portions of the mask pattern which correspond to the first areas;
calculating intensities of light which will be projected on the light exposure area, through use of first portions of the mask pattern, when it is determined that the transmission areas and the non-transmission areas are not mingled; and
dividing each of the first areas into second areas at second intervals smaller than the first intervals and calculating intensities of light which will be projected on the light exposure area, through use of second portions of the mask pattern which correspond to the second areas, when it is determined that the transmission areas and the non-transmission areas are mingled.
According to the fifth aspect of the present invention which aims to attain the aforementioned object, there is provided a program, embedded in a carrier wave, for analyzing light intensity distribution on a light exposure area where a shape of a mask pattern will be projected through an optical system by exposure light coming from a light source, the program executing:
dividing the light exposure area into first areas at predetermined first intervals;
sequentially determining whether transmission areas which transmit the exposure light and non-transmission areas which do not transmit the exposure light are mingled at portions of the mask pattern which correspond to the first areas;
calculating intensities of light which will be projected on the light exposure area, through use of first portions of the mask pattern, when it is determined that the transmission areas and the non-transmission areas are not mingled; and
dividing each of the first areas into second areas at second intervals smaller than the first intervals and calculating intensities of light which will be projected on the light exposure area, through use of second portions of the mask pattern which correspond to the second areas, when it is determined that the transmission areas and the non-transmission areas are mingled.